A new numerical scheme for compressible fluids has recently been presented in Després/CMAME/2023. The method is at the same time a particle method (the mass is lagrangian) and a PDE solver on grid. Since the grid is recalculated at every time step as a Voronoi mesh,the method is  a new instance of a Free-Lagrange solver (a family of method once very popular).  The objective of this presentation will be the exposition of the principles behind the new solver. I will also focus on the role of a "seemingly new" computational geometry formula.